Discontinuity at Fixed Point on Partial S-Metric Spaces

Abstract

This paper examines the idea of partial-S metric spaces, which extend the traditional structure of S-metric spaces. Within this broader framework, we investigate the issue of discontinuity at fixed points—a significant problem originally raised by Rhodes' in the realm of fixed-point theory. We provide sufficient conditions that ensure the existence of fixed points, even when continuity is not assumed. These findings broaden the scope of fixed-point theory, making it applicable to asymmetric topological environments and offering new perspectives on the behavior of discontinuous mappings.